Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Abstract: Compressible cavitating flows arise in physical configurations where rapid pressure variations can drive liquids into metastable states and trigger vapor formation. Simulating these flows is difficult because shock propagation, moving material interfaces, metastable pure-fluid states, and phase change. In addition, cavitation spans scales from unresolved microbubbles to large, resolved vapor regions. A useful numerical framework must preserve conservation, represent the relevant thermodynamic states, allow for phase change, and accommodate the range of cavitation scales. Interface-capturing methods provide a practical route for such calculations, but current formulations remain limited by remnant amounts of absent fluids that can suppress metastability, problem-dependent phase-change thresholds, and required models commonly formulated for different systems of equations. The goal of this thesis is to present a unified framework in which thermodynamic relaxation, subgrid bubble dynamics, and physically based phase-change triggers are brought together consistently. The interface-capturing equations are first reviewed from the parent formulation to the reduced 5- and 6-equation systems, with relaxation processes connecting the hierarchy through mechanical p, thermal T, and chemical-potential µ equilibrium. From this hierarchy, the 5-equation system is selected as the common framework in which the required relaxation and subgrid models are incorporated for the cavitating flows considered in this work. The p- and pT-relaxations are applied to pure and metastable states, and a pTµ-relaxation is developed for liquid--vapor phase change. The resulting algorithm can model pure liquid, pure vapor, their metastable extensions, mass-depleted states, and two-phase equilibrium mixtures without imposing artificial remnant fluids. The framework is tested on canonical problems and experimental configurations, showing that the selected 5-equation implementation reproduces the corresponding 6-equation results with the relaxation procedures in their original setting. The simulations also show that artificial remnant phases can suppress metastable pure-fluid evolution and alter internal pressure-wave dynamics; consequently, relaxation procedures must remain applicable in pure-fluid regions. Finally, a one-way-coupled subgrid bubbly-flow model is adapted to the unified framework and assessed as a physically based phase-change trigger for the cylinder aerobreakup problem. Results show that, although the proposed trigger does not yet correctly capture the physics of cavitation for this problem, it offers a promising path toward physically motivated cavitation onset models.